In this paper, we study the finite energy weak solutions (FEWS) to the interaction problem of compressible viscous fluids and elastic or viscoelastic plates. The notions of relative entropy and relative energy inequality are introduced. First, by utilizing the dissipation effects of the fluid onto the structure, we prove that the additional regularity \(\Delta w \in L_t^2 H_x^s\)  can be obtained, for \(s = s(\gamma ,d,\alpha )>0\) , where \(w\)  is the displacement of the plate, \(\gamma \)  is the adiabatic constant, \(d=2,3\)  is the dimension of the fluid and \(\alpha \)  is the viscoelasticity constant. This is done by following the ideas from [1]}, where similar (but stronger) estimates were obtained for the interaction of a incompressible viscous fluid and a nonlinear Koiter shell. Afterwards, it is proved that all FEWS satisfy the relative energy inequality. Finally, we prove that all FEWS enjoy the weak-strong uniqueness property. The proof uses the strategy from [2]} (see also [3]}, [4]}), and relies on using the relative entropy, which measures the distance between two solutions, and the relative energy inequality, which if tested by sufficiently regular solution of the same problem, gives the desired result by means of the Gronwall lemma. Since the fluid domains of two solutions are not the same in general, the coordinates of both solutions are transformed to the ones of a common fixed domain. The time and space derivatives are then replaced by the corresponding transformed derivatives which depend on the domain transformation, and thus on the displacement of the plate. This drastically increases the difficulty of the analysis. To close these estimates, additional integrability is needed - \(\nabla w \in L_t^2 L_x^\infty \) , which is always ensured by the mentioned regularity \(\Delta w \in L_t^2 H_x^s\)  and the imbedding of Sobolev spaces (for any \(s>0\) ). In the last part of the paper, the obtained results are extended to fluid-structure interaction models for which the structure is more nonlinear. More precisely, we first study the case where the structure is modeled by a semilinear plate model which generalizes Kirchhoff, von Karman and Berger plates (see Appendix for more details). Then, this equation is then replaced by a semilinear thermoelastic system and finally by a quasilinear thermoelastic system, thus furthering the frontiers of the approach presented here.
